8. Let (X, d) be a metric space, and A, B are subset of X, then (i) Fr(A) = A n (A)° A – int A (ii) Fr(A) = o if and only if A is both open and closed (iii) A is closed if and only if A Fr(A)

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
icon
Related questions
Question
8. Let (X, d) be a metric space, and A, B are subset of X, then
(i) Fr(A) = A n (A)° = Ã – int A
A - int A
%D
(ii) Fr(A) = 0 if and only if A is both open and closed
%3D
(iii) A is closed if and only if A Fr(A)
ini
(A mi)
(iv) A is open if and only if A° 2 Fr(A)
(v) Fr(AnB) C Fr(A) U Fr(B). The equality holds if A N B = ¢
(vi) Fr(int A) C Fr(A).
%3D
bas amonoori mort wollo
Transcribed Image Text:8. Let (X, d) be a metric space, and A, B are subset of X, then (i) Fr(A) = A n (A)° = Ã – int A A - int A %D (ii) Fr(A) = 0 if and only if A is both open and closed %3D (iii) A is closed if and only if A Fr(A) ini (A mi) (iv) A is open if and only if A° 2 Fr(A) (v) Fr(AnB) C Fr(A) U Fr(B). The equality holds if A N B = ¢ (vi) Fr(int A) C Fr(A). %3D bas amonoori mort wollo
Expert Solution
steps

Step by step

Solved in 3 steps with 3 images

Blurred answer
Recommended textbooks for you
Advanced Engineering Mathematics
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Mathematics For Machine Technology
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,
Basic Technical Mathematics
Basic Technical Mathematics
Advanced Math
ISBN:
9780134437705
Author:
Washington
Publisher:
PEARSON
Topology
Topology
Advanced Math
ISBN:
9780134689517
Author:
Munkres, James R.
Publisher:
Pearson,